Kinematics - motion

Question 1

Deriving v=u + at

Answer 1

Acceleration = gradient of v-t graph
So change in y / change in x = (v-u)/t
a=(v-u)/t
at=v-u
v=u + at

Question 2

dervive s=1/2 (u+v)t

Answer 2

Displacement = area of v-t graph
Area of trap = (a+b)/2 x h
s= (u+v)/2 x t
s= 1/2(u+v) x t

Question 3

derive s=ut + 1/2 at^2

Answer 3

sub v=u+at into s=1/2(u+v)t
s=1/2(u+u+at)t
s=1/2(2u+at)t
s=u+1/2at^2

Question 4

derive s=vt-1/2at^2

Answer 4

rearrange v=u+at to get u= v-at
sun into s=1/2(u+v)t
s=1/2(v-at+v)t
s=1/2(2v -at)t
s=vt -1/2at^2

Question 5

derive v^2=u^2 +2as

Answer 5

rearrange v=u+at to get t=(v-u)/a
sub into s=1/2(u+v)t
s=1/2(u+v)(v-u/a)
s=1/2a(uv-u^2+v^2-uv)
2as=v^2-u^2
v^2= u^2 + 2as

Question 6

find velocity on s-t graph

Answer 6

the gradient : displacement /time

Question 7

kinetmatic equations at constant speed (a=0)

Answer 7

Distance = speed x time

Question 8

kmph-> ms-1

Answer 8

x1000 dived 60 dived by 60

Question 9

kinematic equations at constant acceleration

Answer 9

SUVATs in formula booklet

Question 10

kinematic equations at variable acceleration

Answer 10

S
V
A
down differnetiate
up interstate

express in terms of t

Question 11

when do you know it’s variable acceleration

Answer 11

expressed in terms of t

Question 12

speed time graphs at constant speed (a=0)

Answer 12

hortizontal line
d=v x t (area under line)

Question 13

speed time graphs at constant acceleration
distance and acceleration

Answer 13

use trap rule for distance = area under line
acceleration = gradient of the line

Question 14

speed time graphs at variable acceleration
shape, distance and accerlatation

Answer 14

curvy line
use intergration for distance = area under the line
acceleration = gradient of line

Question 15

vector motion at constant speed
calculate position vector

Answer 15

position vector = intial position vector + (speed x time)

Question 16

vector motion at constant acceleration

find final velocity and displacement

Answer 16

V = u + at
R =intial postion vector + ut + 1/2at^2
R= intial postion vector + vt -1/2at^2

Question 17

Vector motion at variable acceleration

Answer 17

R
V
A
down differinatiate
up intergrate

Question 18

acceleration in projectiles
horizontal motion and vertical motion

Answer 18

horizontal: a=0
vertical:a= -g

Question 19

how to find speed and direction at a certain point on a projectile

Answer 19

both vertical and horizontal use:
Phythagoras for speed
Tan^-1 for direction

Question 20

vector motion: interpret mathematically “moving in the direction
(2)
(3)”

Answer 20

v= k(2/3)
meaning Parrell to

Question 21

vecotr motion: interpret “is north east of the orgin”

Answer 21

r=k(1)
(1)
some multiple of

Question 22

north east position vectors

Answer 22

i=j

Question 23

north west position vectors

Answer 23

i=-j

Question 24

south east position vectors

Answer 24

i=-j

Question 25

South west position vectors

Answer 25

i=j

Question 26

modelling assumptions: smooth pulley

Answer 26

tension on either side of the pulley is equal

Question 27

modelling assumptions: light string

Answer 27

tension is equal throughout the string

Question 28

modelling assumptions: inextensible string

Answer 28

both particles have same acceleration

Question 29

modelling assumptions: particle

Answer 29

ignore air resistance, ignore rotational effects as no dimensions

Question 30

modelling assumptions: rod

Answer 30

rigid so it doesn’t bend it has no thickness